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Generalized interface models for transport phenomena: unusual scale effects in composite nanomaterials

The effective transport properties of heterogeneous nanoscale materials and structures are affected by several geometrical and physical factors. Among them the presence of imperfect interfaces plays a central role being often at the origin of the scale effects. To describe real contacts between different phases some classical schemes have been introduced in literature, namely the low and the high conducting interface models. Here, we introduce a generalized formalism, which is able to take into account the properties of both previous schemes and, at the same time, it implements more complex behaviors, already observed in recent investigations. We apply our models to the calculation of the effective conductivity in a paradigmatic structure composed of a dispersion of particles. In particular we describe the conductivity dependence upon the size of the inclusions finding an unusual non-monotone scale effect with a pronounced peak at a given particle size. We introduce some intrinsic length scales governing the universal scaling laws.